In flying, to might even hurt you to have Ivy League credentials. Outside of being a pilot, having a degree from the best college you can get into is a good idea. A large part of college is meeting people with different backgrounds and interests and making friends that will last a lifetime.
I can tell you that there have been several occasions for me that I heard about jobs (ouside of flying) and had a crack at them before anyone else because of people I knew from college.
As far as moving quickly along in an aviation career, generally, everyone is looking for experience. A degree may help, but they are much more interested in your experience and what former employers have to say about you. Aviation careers move at a pretty well defined pace. There are exceptions, some from luck and others from hard work, but I doubt any from having a degree from Duke or Stanford.
Degrees from big name schools can be helpful in the business world your first 5 years out of school, but that is about it. After that, it is your talent and skills that drive your salary. From my experience as a pilot, there are limited opportunities to drive revenue or reduce costs for the company you work for, and as such, limited opportunities to differentiate oneself and drive compensation.